(I am going to refer to the comments to your question as well.)
'but the present perfect is hardly used to tell about a finished completed action (all grammar books tell that).'
Please have a look at Present Perfect. Do you still have the impression of hardly used?
The sense of continuity is added to the present perfect tense only if we use it with 'for' resp. 'since'. Well, we're neither asking
'Do you think I could borrow the book after you have finished reading it for two weeks?' (a spark of sense in it)
nor are we asking
'Do you think I could borrow the book after you have finished reading it since today?' (complete nonsense).
That's why we refer to a finished/completed action here.
By the way, we should also consider the assumed length of 'to finish'. While we can easily say 'I have read the book for three months (now).' saying 'I have finished reading the book for three months.' sounds strange because finishing is about coming to an end - unlike living. Therefore, 'I have finished reading the book.' excludes a continuation of the finishing act in the same way as 'He has died.' excludes a continuation of dying - unlike 'I have lived in London.' where living in London can continue.
In addition, the 'do you think' question reveals no uncertainty of temporal kind and is therefore irrelevant for our consideration of the finishedness of the reading act resp. of the present perfect tense. The whole question is not interested in the exact time the act of borrowing could happen. It solely expresses uncertainty caused by possibly existing factors which could render the act of borrowing impossible although the book is theoretically 'borrowable' because the reading is (definitely) finished - factors like the wish to read the book once again or the promise to borrow it to someone else. Of cause, the inquirer wants to have the book as soon as possible. But saying 'after you have finished reading it', they submit to the reading pace of the book owner and, thus, accept the temporal uncertainty in the first place.
